Twisted homology of quantum SL(2)

Details Twisted homology of quantum SL(2) Twisted homology of quantum SL(2)

2004-05-13

arxiv.org/abs/math/0405249v5

K-theory 34, no. 4, 327-360 (2005)

Mathematics

Quantum Algebra

28 pages, no figures, uses package amscd. v5: substantially rewritten

Scientific paper

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators a,b,c,d. We discover a family of automorphisms for which the "twisted" Hochschild dimension coincides with the classical dimension of SL(2, C), thus avoiding the "dimension drop" in Hochschild homology seen for many quantum deformations. Strikingly, the simplest such automorphism is the canonical modular automorphism arising from the Haar functional. In addition, we identify the twisted cyclic cohomology classes corresponding to the three covariant differential calculi over quantum SU(2) discovered by Woronowicz.

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